Details

Time bar (total: 9.1s)

sample38.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms86×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01217
12117
24116
37516
48716
59516
done9516

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
7.0ms
(* (* 3.0 a) c)
5.0ms
(- (* b b) (* (* 3.0 a) c))
33.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
43.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
84.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7s

Counts
72 → 72
Iterations

Useful iterations: 3 (767.0ms)

IterNodesCost
01201001
1279903
21001825
34337821
done5000821

prune184.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3.0 (* a c))
1.0b
(- (* b b) (* 3.0 (* a c)))
1.4b
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
22.6b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
6.0ms
(* 3.0 (* a c))
3.0ms
(- (* b b) (* 3.0 (* a c)))
18.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 3.0 (* a c))
42.0ms
(- (* b b) (* 3.0 (* a c)))
75.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
68.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (357.0ms)

IterNodesCost
0117998
1269902
2839824
32932820
done5001820

prune188.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
1.0b
(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
1.4b
(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
22.6b
(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
9×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt sqrt-prod
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* *-commutative distribute-lft-out--
Counts
4 → 66
Calls
4 calls:
20.0ms
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
3.0ms
(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
18.0ms
(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
4.0ms
(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

series616.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
114.0ms
(- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))
211.0ms
(- (sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c))))) b)
217.0ms
(sqrt (- (* b b) (* (sqrt 3.0) (* (sqrt 3.0) (* a c)))))

simplify481.0ms

Counts
78 → 78
Iterations

Useful iterations: done (479.0ms)

IterNodesCost
01321486
1320985
21109885
done5002881

prune197.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
18.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
18.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
78.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify911.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (232.0ms)

IterNodesCost
0811248
11901104
26001036
320631028
done50001028

prune218.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.3b

regimes245.0ms

Accuracy

84.9% (3.3b remaining)

Error of 15.5b against oracle of 12.2b and baseline of 33.8b

bsearch124.0ms

Steps
ItersRangePoint
9
7.760624497279612e-54
8.046870571685393e-47
2.5407141653924318e-51
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02954
13554
done3554

end0.0ms

sample1.1s

Algorithm
intervals
Results
218.0ms1025×body2560valid
217.0ms5915×body80valid
157.0ms893×body1280valid
99.0ms2995×body80nan
61.0ms447×body640valid
27.0ms107×body5120valid
21.0ms210×body320valid
7.0ms103×body160valid